The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood, through an application of Bayes' theorem. From an epistemological perspective, the posterior probability contains everything there is to know about an uncertain proposition (such as a scientific hypothesis, or parameter values), given prior knowledge and a mathematical model describing the observations available at a particular time. After the arrival of new information, the current posterior probability may serve as the prior in another round of Bayesian updating. In the context of Bayesian statistics, the posterior probability distribution usually describes the epistemic uncertainty about statistical parameters conditional on a collection of observed data. From a given posterior distribution, various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest posterior density interval (HPDI). But while conceptually simple, the posterior distribution is generally not tractable and therefore needs to be either analytically or numerically approximated. (Wikipedia).
35 - Normal prior and likelihood - posterior predictive distribution
This video provides a derivation of the normal posterior predictive distribution for the case of a normal prior distribution and likelihood. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4o
From playlist Bayesian statistics: a comprehensive course
29 - Posterior predictive distribution: example Disease
This video provides an introduction to the concept of posterior predictive distributions, using the example of disease prevalence in a population. Here we consider the case of a beta prior and binomial likelihood; resulting in a beta-binomial posterior. If you are interested in seeing mo
From playlist Bayesian statistics: a comprehensive course
Learn to find the or probability from a tree diagram
👉 Learn how to find the conditional probability of an event. Probability is the chance of an event occurring or not occurring. The probability of an event is given by the number of outcomes divided by the total possible outcomes. Conditional probability is the chance of an event occurring
From playlist Probability
How to find the probability of consecutive events
👉 Learn how to find the conditional probability of an event. Probability is the chance of an event occurring or not occurring. The probability of an event is given by the number of outcomes divided by the total possible outcomes. Conditional probability is the chance of an event occurring
From playlist Probability
Finding the conditional probability from a two way frequency table
👉 Learn how to find the conditional probability of an event. Probability is the chance of an event occurring or not occurring. The probability of an event is given by the number of outcomes divided by the total possible outcomes. Conditional probability is the chance of an event occurring
From playlist Probability
Finding the conditional probability from a tree diagram
👉 Learn how to find the conditional probability of an event. Probability is the chance of an event occurring or not occurring. The probability of an event is given by the number of outcomes divided by the total possible outcomes. Conditional probability is the chance of an event occurring
From playlist Probability
Ex: Determine Conditional Probability from a Table
This video provides two examples of how to determine conditional probability using information given in a table.
From playlist Probability
(New Version Available) Conditional Probability
New Version: Fixes an error at 7:00: https://youtu.be/WgsxhWPAo4c This video explains how to determine conditional probability. http://mathispower4u.yolasite.com/
From playlist Counting and Probability
How to find the conditional probability from a tree diagram
👉 Learn how to find the conditional probability of an event. Probability is the chance of an event occurring or not occurring. The probability of an event is given by the number of outcomes divided by the total possible outcomes. Conditional probability is the chance of an event occurring
From playlist Probability
DeepMind x UCL | Deep Learning Lectures | 11/12 | Modern Latent Variable Models
This lecture, by DeepMind Research Scientist Andriy Mnih, explores latent variable models, a powerful and flexible framework for generative modelling. After introducing this framework along with the concept of inference, which is central to it, Andriy focuses on two types of modern latent
From playlist Learning resources
18. Bayesian Statistics (cont.)
MIT 18.650 Statistics for Applications, Fall 2016 View the complete course: http://ocw.mit.edu/18-650F16 Instructor: Philippe Rigollet In this lecture, Prof. Rigollet talked about Bayesian confidence regions and Bayesian estimation. License: Creative Commons BY-NC-SA More information at
From playlist MIT 18.650 Statistics for Applications, Fall 2016
Machine learning - Importance sampling and MCMC I
Importance sampling and Markov chain Monte Carlo (MCMC). Application to logistic regression. Slides available at: http://www.cs.ubc.ca/~nando/540-2013/lectures.html Course taught in 2013 at UBC by Nando de Freitas
From playlist Machine Learning 2013
Bayesian Statistics: An Introduction
See all my videos here: http://www.zstatistics.com/videos/ 0:00 Introduction 2:25 Frequentist vs Bayesian 5:55 Bayes Theorum 10:45 Visual Example 15:05 Bayesian Inference for a Normal Mean 24:30 Conjugate priors 32:55 Credible Intervals
From playlist Statistical Inference (7 videos)
Kerrie Mengersen: Bayesian Modelling
Abstract: This tutorial will be a beginner’s introduction to Bayesian statistical modelling and analysis. Simple models and computational tools will be described, followed by a discussion about implementing these approaches in practice. A range of case studies will be presented and possibl
From playlist Probability and Statistics
DSI Seminar | Adaptive Contraction Rates and Model Selection Consistency of Variational Posteriors
In this DSI Seminar Series talk from June 2021, University of Notre Dame associate professor Lizhen Li discusses adaptive inference based on variational Bayes. Abstract: We propose a novel variational Bayes framework called adaptive variational Bayes, which can operate on a collection of
From playlist DSI Virtual Seminar Series
SLT Supplemental - Seminar 2 - Markov Chain Monte Carlo
This series provides supplemental mathematical background material for the seminar on Singular Learning Theory. In this seminar Liam Carroll introduces us to Markov Chain Monte Carlo, a method for sampling from the Bayesian posterior. The webpage for this seminar is http://metauni.org/pos
From playlist Metauni
O'Reilly Webcast: Bayesian Statistics Made Simple
Join Allen Downey, author of Think Stats: Probability and Statistics for Programmers for an introduction to Bayesian statistics using Python. Bayesian statistical methods are becoming more common and more important, but there are not many resources to help beginners get started. People who
From playlist O'Reilly Webcasts 2
Statistical Rethinking 2022 Lecture 02 - Bayesian Inference
Bayesian updating, sampling posterior distributions, computing posterior and prior predictive distributions Course materials: https://github.com/rmcelreath/stat_rethinking_2022 Intro music: https://www.youtube.com/watch?v=QH_VKWStK98 Chapters: 00:00 Introduction 04:53 Garden of forking
From playlist Statistical Rethinking 2022
Using a contingency table to find the conditional probability
👉 Learn how to find the conditional probability of an event. Probability is the chance of an event occurring or not occurring. The probability of an event is given by the number of outcomes divided by the total possible outcomes. Conditional probability is the chance of an event occurring
From playlist Probability